THE TRANSPORTATION OF GASES
153
tances in percentages of the pressure which the fan will exert with its outlet completely closed; this latter pressure with a few exceptions is the maximum pressure a fan will exert at any given speed, and is symbolized S.N.D. Four curves are plotted, using as ordinates (1) the ratio of the velocity through the fan outlet to the peripheral speed of the wheel and designated V/T; (2) the mechanical efficiency E; (3) the ratio of I',
JOO JO
20 .30 M .50 .60 JO M Maintained JJeslstanc? In % of S.N*Oj
FIG. 3.—Characteristic curves of a steel-plate paddle-wheel fan.
,10 20 .30- 40 .50 .60 .70 £0 30 •Discharge Opening In X of Full Cutler Area.
FIG. 4.
impact pressure to S.N.D., designated fe/S.N.D.; and (4) the ratio of static pressure to impact pressure, designated hjhi. From these curves can be computed the performance of any size of symmetrical fan under any conditions of pressure, volume or speed within its structural possibilities.
As an example of how these curves are applied, let it be assumed that a size of fan is required which will operate most efficiently when delivering 10,000 cu. ft. per minute against 2 in. static pressure. Assume the fan to operate at a mechanical efficiency of 50 per cent. At this efficiency the abscissa /is/S.N.D. is 0.857, from which S.N.D. = 2.0/0.857 = 2.33 in. For the same efficiency 7i;/S.N.D. = 0.923, therefore^ = 0.923 X 2.33 = 2.15 in.; h = h8 + h, hence h = 0.15 in.; and V = 4000\/ 0.15= 1,548 ft. per minute. For 10,000 cu. ft. per minute the area of the fan outlet must then be 6.47 sq. ft. Knowing that for this particular design of fan the outlet area is expressed by the equation A = 0.306D2, the diameter D is found to be 4.59 ft. Corresponding to A./S.N.D. = 0.857 is found a value of V/T = 0.298, from which the peripheral speed = 1,548/0.298 = 5,200 ft. per minute, and the speed of the fan is computed as 360 r.p.m. The other dimensions of the fan are found from the basis of design, in which these dimensions should be expressed as functions of the diameter of the wheel D. Air horsepower = a.hp. = 10,000 X 2.15 X 5.2/-33,000 = 3.39; b.hp. = 3.39/0.50 = 6.78.
As a second example suppose a fan with a wheel 3 ft. in diameter is to deliver 5,000 cu. ft. per minute against 2 in. maintained resistance or static pressure, leaving revolutions per minute and brake horsepower to be determined. From the equation A = 0.306/)2, A = 2.76 sq. ft., therefore V ~ 1,810 ft. per minute. From V = 4,000-\A,~/i = 0.205 in. making hi = 2.205 in. Here ha/hi = 0.907, at which point on the curves of Fig. 1 V/T = 0.322; hence T = 5,620 ft. per minute. As D = 3 ft., r.p.m. = 597. a.hp. = 5,000 X 2.205 X 5.2/33,000 = 1.74. From the curves E — 49.2 per cent, hence b.hp. = 3.54.
The curves of Fig. 3 may also be plotted using for abscissas the static pressures or maintained resistances expressed in percentages of the pressure which would result from a velocity equal to the peripheral or tip speed of the blades and which is referred to as tip-speed pressure.
Discharge Opening in Percentage of Full Outlet.—Figure 4 is for the same fan as Fig. 3 and shows the same ordinates plotted against the discharge outlet area